# The Distributive Property

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The Distributive Property

The Distributive Property The distributive property is mental math strategy that can be used when multiplying. 43 x 5 =? Break apart the double-digit number. 43 x 5 =? 40 + 3 Then multiply each part by 5. 43 x 5 =? 40 x5 + 3 x5 Then multiply each part by 5. 43 x 5 =? 40 x5 200 + 3 x5 15 Finally, sum your two products 43 x 5 =215 40 + 3 x5 x5 200 + 15 = 215 Let’s look at another example. 53 x 6 = ? Break apart the double-digit number. 53 x 6 = ? Break apart the double-digit number. 53 x 6 = ? 50 + 3 Multiply each part by 6. 53 x 6 = ? 50 x6 + 3 x6 Multiply each part by 6. 53 x 6 = ? 50 x6 300 + 3 x6 18 Sum the two products. 53 x 6 = 318 50 + 3 x6 x6 300 + 18 = 318 There are three steps to the distributive property. 4 x 28 = There are three steps to the distributive property. 4 x 28 = 1) Break apart the double-digit number. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) 1) Break apart the double-digit number. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) 1) Break apart the double-digit number. 2) Multiply each part by 4. (distribute the 4) There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8) 1) Break apart the double-digit number. 2) Multiply each part by 4. (distribute the 4) There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8) 1) Break apart the double-digit number. 2) Multiply each part by 4. (distribute the 4) 3) Sum the two products. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = 80 + (4 x 8) 1) Break apart the double-digit number. 2) Multiply each part by 4. (distribute the 4) 3) Sum the two products. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = 80 + 32 1) Break apart the double-digit number. 2) Multiply each part by 4. (distribute the 4) 3) Sum the two products. There are three steps to the distributive property. 4 x 28 = 4 x (20 + 8) = 80 + 32 = 112 1) Break apart the double-digit number. 2) Multiply each part by 4. (distribute the 4) 3) Sum the two products. The word “distribute” means “to give out.” Distribute the cubes to the girls. Distribute the cubes to the girls. Distribute the cubes to the girls. Distribute the cubes to the girls. Distribute the cubes to the girls. Distribute the cubes to the girls. In this example, the 5 was distributed. 5 x 38 = 5 x (30 + 8) = (5 x 30) + (5 x 8) In this example, the 7 was distributed. 7 x 46 = 7 x (40 + 6) = (7 x 40) + (7 x 6) Find the area of the rectangle. Area = length x width 6 ft 24 ft Find the area of the rectangle. Area = length x width 6 ft 24 ft Find the area of the rectangle. Area = length x width 6 ft 20 ft + 4 ft Find the area of the rectangle. Area = length x width 6 ft 20 ft + 4 ft Find the area of the rectangle. Area = length x width 6 ft 6 ft 20 ft + 4 ft Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 ft 20 ft + 4 ft Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 x 20 = 120 sq ft 20 ft 6 ft + 4 ft Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 x 20 = 120 sq ft 6 ft 6 x 4 = 24 sq ft 20 ft + 4 ft Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 120 sq ft 20 ft 6 ft + 24 sq ft 4 ft Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft 20 ft 6 ft + 24 sq ft 4 ft Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft 20 ft 24 sq ft + 4 ft Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft 20 ft 24 sq ft + 4 ft Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft + 24 sq ft 24 ft Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 144 sq ft 24 ft A swimming pool has a shallow end and a deep end. Find the surface area of the pool. 8 yds deep water shallow water 5 yds 10 yds Break the pool into a deep end and a shallow end. 8 yds deep water 5 yds 8 yds shallow water 10 yds Find the area of the deep end. 8 yds deep water 5 yds 8 yds shallow water 10 yds Find the area of the deep end. 8 yds 8x5 = 40 5 yds 8 yds shallow water 10 yds Find the area of the shallow end. 8 yds 8x5 = 40 5 yds 8 yds shallow water 10 yds Find the area of the shallow end. 8 yds 8x5 = 40 5 yds 8 yds 8 x 10 = 80 10 yds Now sum the two areas together. 8 yds 8x5 = 40 5 yds 8 yds 8 x 10 = 80 10 yds Now sum the two areas together. 8 yds 40 5 yds + 80 10 yds 40 + 80 = 120 square yards 8 yds 40 80 5 yds 10 yds Write an expression that shows how to find the area of the rectangle and uses the distributive property. 9 yds 5 yds 20 yds Find the areas for each individual rectangle. 9 yds 5 yds 20 yds Find the areas for each individual rectangle. 9 yds (9 x 5) 5 yds 20 yds Find the areas for each individual rectangle. 9 yds (9 x 5) 5 yds (9 x 20) 20 yds Sum the two areas. 9 yds (9 x 5) 5 yds + (9 x 20) 20 yds (9 x 5) + (9 x 20) = area 9 yds (9 x 5) 5 yds (9 x 20) 20 yds Practice Time 1) Which of the following expressions shows the distributive property for 5 x (3 + 7)? (5 + 3) x (5 + 7) (5 x 3) x (5 x 7) (5 x 3) + (5 x 7) 1) Which of the following expressions shows the distributive property for 5 x (3 + 7)? Correct! (5 x 3) + (5 x 7) 2) Which of the following expressions shows the distributive property for 3 x (9 + 4) ? (3 x 9) + (3 x 4) (3 + 9) + (3 + 4) (3 + 9) x (3 + 4) 2) Which of the following expressions shows the distributive property for 3 x (9 + 4) ? (3 x 9) + (3 x 4) Correct! 3) Which of the following expressions is equivalent to: 2+3+2+3 and shows the distributive property. 2+2+3+3 2 x (2 + 3) 3 x (2 + 3) 3) Which of the following expressions is equivalent to: 2+3+2+3 and uses the distributive property. 2 x (2 + 3) Correct! 4) Which of the following expressions is equivalent to: (4 x 3) + (4 x 8) ? 3 x (4 + 8) 8 x (3 + 4) 4 x (3 + 8) 4) Which of the following expressions is equivalent to: (4 x 3) + (4 x 8) ? Correct! 4 x (3 + 8) 5) Which of the following expressions is equivalent to: (5 x 9) + (5 x 3) ? 3 x (9 + 5) 5 x (9 + 3) 9 x (3 + 5) 5) Which of the following expressions is equivalent to: (5 x 9) + (5 x 3) ? 5 x (9 + 3) Correct! 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 3 yds 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 4 yds 3 yds 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 4x3 3 yds 4 yds 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 yds 4x3 3 yds 4 yds 4x9 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4x3 4 yds 4x9 4 yds 3 yds 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4x3 4x9 4 yds 3 yds 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4x3 4x9 4 yds 3 yds 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4x3 + 4x9 4 yds 3 yds 9 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 4 yds 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 6 yds 4 yds 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 6x4 4 yds 6 yds 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 6x4 4 yds 6 yds 6x8 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6x4 6 yds 6x8 6 yds 4 yds 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6x4 6x8 6 yds 4 yds 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6x4 6x8 6 yds 4 yds 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6x4 + 6x8 6 yds 4 yds 8 yds 8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 2 yds 10 yds 8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 5x2 2 yds 5 x 10 10 yds 8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 x 2 + 5 x 10 5 yds 2 yds 10 yds 9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 3 yds 5 yds 9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 8x3 3 yds 8x5 5 yds 9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8x3 + 8x5 8 yds 3 yds 5 yds 10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds x yds 10 yds 10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5 yds 5x x yds 5 ∙ 10 10 yds 10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5x + 5 ∙ 10 5 yds x yds 10 yds 11) Which expression is equivalent to 3(x + 7)? x + 10 x + 21 3x + 7 3x + 21 11) Which expression is equivalent to 3(x + 7)? 3x + 21 Correct! 12) Which expression is equivalent to 4(x + 5)? x+9 4x + 20 4x + 5 9x 12) Which expression is equivalent to 4(x + 5)? 4x + 20 Correct! 13) Which expression is equivalent to 8(x + 2)? 10x 8x + 2 8x + 16 8x + 10 13) Which expression is equivalent to 8(x + 2)? 8x + 16 Correct! 14) Which expression is equivalent to 2(x + 3)? 2x + 6 2x + 5 2x + 3 2x + 2 14) Which expression is equivalent to 2(x + 3)? 2x + 6 Correct! The End.